Research

28 pages, 8107 KiB

Open AccessArticle

Parameter Estimation, Robust Controller Design and Performance Analysis for an Electric Power Steering System

by Van Giao Nguyen, Xuexun Guo, Chengcai Zhang and Xuan Khoa Tran

Algorithms 2019, 12(3), 57; https://doi.org/10.3390/a12030057 - 05 Mar 2019

Cited by 6 | Viewed by 6060

This paper presents a parameter estimation, robust controller design and performance analysis for an electric power steering (EPS) system. The parametrical analysis includes the EPS parameters and disturbances, such as the assist motor parameters, sensor-measurement noise, and random road factors, allowing the EPS [...] Read more.

This paper presents a parameter estimation, robust controller design and performance analysis for an electric power steering (EPS) system. The parametrical analysis includes the EPS parameters and disturbances, such as the assist motor parameters, sensor-measurement noise, and random road factors, allowing the EPS stability to be extensively investigated. Based on the loop-shaping technique, the system controller is designed to increase the EPS stability and performance. The loop-shaping procedure is proposed to minimize the influence of system disturbances on the system outputs. The simplified refined instrumental variable (SRIV) algorithm, least squares state variable filter (LSSVF) algorithm and instrumental variable state variable filter (IVSVF) algorithm are applied to reduce the model mismatching between the theoretical EPS models and the real EPS model, as the EPS parameters can be accurately identified based on the experimental EPS data. The performance of the proposed method is thus compared to that of the proportional-integral-derivative (PID) test bench results for the EPS system. The experimental results demonstrated that the proposed loop-shaping controller provides good tracking performance while ensuring the stability of the EPS system. Full article

(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)

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19 pages, 592 KiB

Open AccessArticle

Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

by Yong-Hong Lan, Jun-Jun Xia and Yue-Xiang Shi

Algorithms 2019, 12(1), 20; https://doi.org/10.3390/a12010020 - 10 Jan 2019

Cited by 17 | Viewed by 3987

Abstract

In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L [...] Read more.

In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method. Full article

(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)

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17 pages, 828 KiB

Open AccessArticle

Parametric Estimation in the Vasicek-Type Model Driven by Sub-Fractional Brownian Motion

by Shengfeng Li and Yi Dong

Algorithms 2018, 11(12), 197; https://doi.org/10.3390/a11120197 - 04 Dec 2018

Cited by 5 | Viewed by 2996

Abstract

In the paper, we tackle the least squares estimators of the Vasicek-type model driven by sub-fractional Brownian motion:

d X_{t} = (μ + θ X_{t}) d t + d S_{t}^{H}, t \geq 0

with [...] Read more.

In the paper, we tackle the least squares estimators of the Vasicek-type model driven by sub-fractional Brownian motion:

d X_{t} = (μ + θ X_{t}) d t + d S_{t}^{H}, t \geq 0

with

X_{0} = 0

, where

S^{H}

is a sub-fractional Brownian motion whose Hurst index H is greater than

\frac{1}{2}

, and

μ \in R

,

θ \in R^{+}

are two unknown parameters. Based on the so-called continuous observations, we suggest the least square estimators of

μ

and

θ

and discuss the consistency and asymptotic distributions of the two estimators. Full article

(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)

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14 pages, 338 KiB

Open AccessArticle

Iterative Identification for Multivariable Systems with Time-Delays Based on Basis Pursuit De-Noising and Auxiliary Model

by Junyao You and Yanjun Liu

Algorithms 2018, 11(11), 180; https://doi.org/10.3390/a11110180 - 06 Nov 2018

Cited by 6 | Viewed by 2392

Abstract

This paper focuses on the joint estimation of parameters and time-delays of the multiple-input single-output output-error systems. Since the time-delays are unknown, an effective identification model with a high dimensional and sparse parameter vector is established based on overparameterization. Then, the identification problem [...] Read more.

This paper focuses on the joint estimation of parameters and time-delays of the multiple-input single-output output-error systems. Since the time-delays are unknown, an effective identification model with a high dimensional and sparse parameter vector is established based on overparameterization. Then, the identification problem is converted to a sparse optimization problem. Based on the basis pursuit de-noising criterion and the auxiliary model identification idea, an auxiliary model based basis pursuit de-noising iterative algorithm is presented. The parameters are estimated by solving a quadratic program, and the unavailable terms in the information vector are updated by the auxiliary model outputs iteratively. The time-delays are estimated according to the sparse structure of the parameter vector. The proposed method can obtain effective estimates of the parameters and time-delays from few sampled data. The simulation results illustrate the effectiveness of the proposed algorithm. Full article

(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)

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17 pages, 698 KiB

Open AccessArticle

The Bias Compensation Based Parameter and State Estimation for Observability Canonical State-Space Models with Colored Noise

by Xuehai Wang, Feng Ding, Qingsheng Liu and Chuntao Jiang

Algorithms 2018, 11(11), 175; https://doi.org/10.3390/a11110175 - 01 Nov 2018

Cited by 1 | Viewed by 2690

Abstract

This paper develops a bias compensation-based parameter and state estimation algorithm for the observability canonical state-space system corrupted by colored noise. The state-space system is transformed into a linear regressive model by eliminating the state variables. Based on the determination of the noise [...] Read more.

This paper develops a bias compensation-based parameter and state estimation algorithm for the observability canonical state-space system corrupted by colored noise. The state-space system is transformed into a linear regressive model by eliminating the state variables. Based on the determination of the noise variance and noise model, a bias correction term is added into the least squares estimate, and the system parameters and states are computed interactively. The proposed algorithm can generate the unbiased parameter estimate. Two illustrative examples are given to show the effectiveness of the proposed algorithm. Full article

(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)

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12 pages, 408 KiB

Open AccessArticle

Parameter Estimation of a Class of Neural Systems with Limit Cycles

by Xuyang Lou, Xu Cai and Baotong Cui

Algorithms 2018, 11(11), 169; https://doi.org/10.3390/a11110169 - 26 Oct 2018

Cited by 2 | Viewed by 2174

Abstract

This work addresses parameter estimation of a class of neural systems with limit cycles. An identification model is formulated based on the discretized neural model. To estimate the parameter vector in the identification model, the recursive least-squares and stochastic gradient algorithms including their [...] Read more.

This work addresses parameter estimation of a class of neural systems with limit cycles. An identification model is formulated based on the discretized neural model. To estimate the parameter vector in the identification model, the recursive least-squares and stochastic gradient algorithms including their multi-innovation versions by introducing an innovation vector are proposed. The simulation results of the FitzHugh–Nagumo model indicate that the proposed algorithms perform according to the expected effectiveness. Full article

(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)

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10 pages, 2579 KiB

Open AccessArticle

Online Adaptive Parameter Estimation for Quadrotors

by Jun Zhao, Xian Wang, Guanbin Gao, Jing Na, Hongping Liu and Fujin Luan

Algorithms 2018, 11(11), 167; https://doi.org/10.3390/a11110167 - 25 Oct 2018

Cited by 9 | Viewed by 2783

Abstract

The stability and robustness of quadrotors are always influenced by unknown or immeasurable system parameters. This paper proposes a novel adaptive parameter estimation technology to obtain high-accuracy parameter estimation for quadrotors. A typical mathematical model of quadrotors is first obtained, which can be [...] Read more.

The stability and robustness of quadrotors are always influenced by unknown or immeasurable system parameters. This paper proposes a novel adaptive parameter estimation technology to obtain high-accuracy parameter estimation for quadrotors. A typical mathematical model of quadrotors is first obtained, which can be used for parameter estimation. Then, an expression of the parameter estimation error is derived by introducing a set of auxiliary filtered variables. Moreover, an augmented matrix is constructed based on the obtained auxiliary filtered variables, which is then used to design new adaptive laws to achieve exponential convergence under the standard persistent excitation (PE) condition. Finally, a simulation and an experimental verification for a typical quadrotor system are shown to illustrate the effectiveness of the proposed method. Full article

(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)

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15 pages, 1199 KiB

Open AccessArticle

Estimating the Volume of the Solution Space of SMT(LIA) Constraints by a Flat Histogram Method

by Wei Gao, Hengyi Lv, Qiang Zhang and Dunbo Cai

Algorithms 2018, 11(9), 142; https://doi.org/10.3390/a11090142 - 18 Sep 2018

Cited by 1 | Viewed by 3006

Abstract

The satisfiability modulo theories (SMT) problem is to decide the satisfiability of a logical formula with respect to a given background theory. This work studies the counting version of SMT with respect to linear integer arithmetic (LIA), termed SMT(LIA). Specifically, the purpose of [...] Read more.

The satisfiability modulo theories (SMT) problem is to decide the satisfiability of a logical formula with respect to a given background theory. This work studies the counting version of SMT with respect to linear integer arithmetic (LIA), termed SMT(LIA). Specifically, the purpose of this paper is to count the number of solutions (volume) of a SMT(LIA) formula, which has many important applications and is computationally hard. To solve the counting problem, an approximate method that employs a recent Markov Chain Monte Carlo (MCMC) sampling strategy called “flat histogram” is proposed. Furthermore, two refinement strategies are proposed for the sampling process and result in two algorithms, MCMC-Flat^1/2 and MCMC-Flat^1/t, respectively. In MCMC-Flat^1/t, a pseudo sampling strategy is introduced to evaluate the flatness of histograms. Experimental results show that our MCMC-Flat^1/t method can achieve good accuracy on both structured and random instances, and our MCMC-Flat^1/2 is scalable for instances of convex bodies with up to 7 variables. Full article

(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)

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